Optimal polygonal interpolation
Jiří Kobza (1999)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Jiří Kobza (1999)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Rack, Heinz-Joachim, Vajda, Robert (2014)
Serdica Journal of Computing
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ACM Computing Classification System (1998): G.1.1, G.1.2. We consider optimal Lagrange interpolation with polynomials of degree at most two on the unit interval [−1, 1]. In a largely unknown paper, Schurer (1974, Stud. Sci. Math. Hung. 9, 77-79) has analytically described the infinitely many zero-symmetric and zero-asymmetric extremal node systems −1 ≤ x1 < x2 < x3 ≤ 1 which all lead to the minimal Lebesgue constant 1.25 that had already been determined by Bernstein...
Cetin Kaya Koc, Guanrong Chen (1993)
Numerische Mathematik
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Wu, Jinming, Zhang, Xiaolei, Peng, Lihui (2010)
Mathematical Problems in Engineering
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Jiří Fiala (1971)
Aplikace matematiky
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Robert Schaback (1982)
Mathematische Zeitschrift
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Marco, Ana, Martínez, José-Javier (2008)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Simian, Dana, Simian, Corina (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Jan S. Hesthaven, Benjamin Stamm, Shun Zhang (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We propose two new algorithms to improve greedy sampling of high-dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the development of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a saturation assumption of the error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard...